Asymptotically Hilbertian Modular Banach Spaces: Examples of Uncountable Categoricity

We give a criterion ensuring that the elementary class of a modular Banach space E (that is, the class of Banach spaces, some ultrapower of which is linearly isometric to an ultrapower of E) consists of all direct sums E\oplus_m H, where H is an arbitrary Hilbert space and \oplus_m denotes the modular direct sum. Also, we give several families of examples in the class of Nakano direct sums of finite dimensional normed spaces that satisfy this criterion. This yields many new examples of uncountably categorical Banach spaces, in the model theory of Banach space structures.Comment: 20 page

Non-stationary Spectra of Local Wave Turbulence

The evolution of the Kolmogorov-Zakharov (K-Z) spectrum of weak turbulence is studied in the limit of strongly local interactions where the usual kinetic equation, describing the time evolution of the spectral wave-action density, can be approximated by a PDE. If the wave action is initially compactly supported in frequency space, it is then redistributed by resonant interactions producing the usual direct and inverse cascades, leading to the formation of the K-Z spectra. The emphasis here is on the direct cascade. The evolution proceeds by the formation of a self-similar front which propagates to the right leaving a quasi-stationary state in its wake. This front is sharp in the sense that the solution remains compactly supported until it reaches infinity. If the energy spectrum has infinite capacity, the front takes infinite time to reach infinite frequency and leaves the K-Z spectrum in its wake. On the other hand, if the energy spectrum has finite capacity, the front reaches infinity within a finite time, t*, and the wake is steeper than the K-Z spectrum. For this case, the K-Z spectrum is set up from the right after the front reaches infinity. The slope of the solution in the wake can be related to the speed of propagation of the front. It is shown that the anomalous slope in the finite capacity case corresponds to the unique front speed which ensures that the front tip contains a finite amount of energy as the connection to infinity is made. We also introduce, for the first time, the notion of entropy production in wave turbulence and show how it evolves as the system approaches the stationary K-Z spectrum.Comment: revtex4, 19 pages, 10 figure

First-principles approach to rotational-vibrational frequencies and infrared intensity for H2_2 adsorbed in nanoporous materials

The absorption sites and the low-lying rotational and vibrational (RV) energy states for H$_2$ adsorbed within a metal-organic framework are calculated via van der Waals density functional theory. The induced dipole due to bond stretching is found to be accurately given by a first-principles driven approximation using maximally-localized-Wannier-function analysis. The strengths and positions of lines in the complex spectra of RV transitions are in reasonable agreement with experiment, and in particular explain the experimentally mysteriously missing primary line for para hydrogen

Criterion for universality class independent critical fluctuations: example of the 2D Ising model

Order parameter fluctuations for the two dimensional Ising model in the region of the critical temperature are presented. A locus of temperatures T*(L) and of magnetic fields B*(L) are identified, for which the probability density function is similar to that for the 2D-XY model in the spin wave approximation.The characteristics of the fluctuations along these points are largely independent of universality class. We show that the largest range of fluctuations relative to the variance of the distribution occurs along these loci of points, rather than at the critical temperature itself and we discuss this observation in terms of intermittency. Our motivation is the identification of a generic form for fluctuations in correlated systems in accordance with recent experimental and numerical observations. We conclude that a universality class dependent form for the fluctuations is a particularity of critical phenomena related to the change in symmetry at a phase transition.Comment: to appear in Phys. Rev.

Principles and Implementation of Deductive Parsing

We present a system for generating parsers based directly on the metaphor of parsing as deduction. Parsing algorithms can be represented directly as deduction systems, and a single deduction engine can interpret such deduction systems so as to implement the corresponding parser. The method generalizes easily to parsers for augmented phrase structure formalisms, such as definite-clause grammars and other logic grammar formalisms, and has been used for rapid prototyping of parsing algorithms for a variety of formalisms including variants of tree-adjoining grammars, categorial grammars, and lexicalized context-free grammars.Comment: 69 pages, includes full Prolog cod

Solvable rational extensions of the Morse and Kepler-Coulomb potentials

We show that it is possible to generate an infinite set of solvable rational extensions from every exceptional first category translationally shape invariant potential. This is made by using Darboux-B\"acklund transformations based on unphysical regular Riccati-Schr\"odinger functions which are obtained from specific symmetries associated to the considered family of potentials